Question

An air-filled pipe is found to have successive harmonics at 435 Hz , 725 Hz , and 1015 Hz . It is unknown whether harmonics below 435 Hz and above 1015 Hz exist in the pipe. What is the length of the pipe?

Answer 1

L = 1.706 m

Step-by-step explanation:

Three successive harmonics in the pipe is given as

`f_1 = 435 Hz`

`f_2 = 725 Hz`

`f_3 = 1015 Hz`

now if we take the ratio of all frequency

then we have

f1 : f2 : f3 = 435 : 725 : 1015 = 3 : 5 : 7

since the ratio of consecutive frequency is in ratio of odd numbers so this must be 3rd harmonics, 5th harmonics and 7 harmonics

And as per the formula we have

`f_1 = (3v)/(4L)`

`435 = (3(340))/(4L)`

`L = 1.706 m`